Related papers: Space-filling design for nonlinear models
In this paper we construct nonlinear partial differential equations in more than 3 independent variables, possessing a manifold of analytic solutions with high, but not full, dimensionality. For this reason we call them ``partially…
Motivated by the problem of optimization of force-field systems in physics using large-scale computer simulations, we consider exploration of a deterministic complex multivariate response surface. The objective is to find input combinations…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
The dynamic emulation of non-linear deterministic computer codes where the output is a time series, possibly multivariate, is examined. Such computer models simulate the evolution of some real-world phenomenon over time, for example models…
Using the mathematical framework of information geometry, we introduce a novel method which allows one to efficiently determine the exact shape of simultaneous confidence regions for non-linearly parametrised models. Furthermore, we show…
Insightful interdisciplinary collaboration is essential to the principled governance of technology. When such efforts address the interaction between computation and society, they often focus on modeling, the process by which computer…
Generative models have enjoyed widespread success in a variety of applications. However, they encounter inherent mathematical limitations in modeling distributions where samples are constrained by equalities, as is frequently the setting in…
Traditional projection-based reduced-order modeling approximates the full-order model by projecting it onto a linear subspace. With a fast-decaying Kolmogorov $n$-width of the solution manifold, the resulting reduced-order model (ROM) can…
The need for application-specific design of multicore/manycore processing platforms is evident with computing systems finding use in diverse application domains. In order to tailor multicore/manycore processors for application specific…
Computer models play a key role in many scientific and engineering problems. One major source of uncertainty in computer model experiment is input parameter uncertainty. Computer model calibration is a formal statistical procedure to infer…
Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…
Theoretical concepts in condensed matter physics are typically verified and also developed by exploiting computer simulations mostly in simple models. Predictions based on these usually isotropic models are often at odds with measurement…
In computational design and fabrication, neural networks are becoming important surrogates for bulky forward simulations. A long-standing, intertwined question is that of inverse design: how to compute a design that satisfies a desired…
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…
We propose a new approach for identifying the support points of a locally optimal design when the model is a nonlinear model. In contrast to the commonly used geometric approach, we use an approach based on algebraic tools. Considerations…
We propose confidence regions for the parameters of incomplete models with exact coverage of the true parameter in finite samples. Our confidence region inverts a test, which generalizes Monte Carlo tests to incomplete models. The test…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
Numerical simulations have revolutionized the industrial design process by reducing prototyping costs, design iterations, and enabling product engineers to explore the design space more efficiently. However, the growing scale of simulations…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
Instructional designers face an overwhelming array of design choices, making it challenging to identify the most effective interventions. To address this issue, I propose the concept of a Model Human Learner, a unified computational model…